Microwave spectroscopic study of the hyperfine structure of antiprotonic helium-3

In this work we describe the latest results for the measurements of the hyperfine structure of antiprotonic helium-3. Two out of four measurable super-super-hyperfine SSHF transition lines of the (n,L)=(36,34) state of antiprotonic helium-3 were observed. The measured frequencies of the individual transitions are 11.12548(08) GHz and 11.15793(13) GHz, with an increased precision of about 43% and 25% respectively compared to our first measurements with antiprotonic helium-3 [S. Friedreich et al., Phys. Lett. B 700 (2011) 1--6]. They are less than 0.5 MHz higher with respect to the most recent theoretical values, still within their estimated errors. Although the experimental uncertainty for the difference of 0.03245(15) GHz between these frequencies is large as compared to that of theory, its measured value also agrees with theoretical calculations. The rates for collisions between antiprotonic helium and helium atoms have been assessed through comparison with simulations, resulting in an elastic collision rate of gamma_e = 3.41 +- 0.62 MHz and an inelastic collision rate of gamma_i = 0.51 +- 0.07 MHz.

super-hyperfine (SHF) splitting, which can be characterized by the angular momentum Sp. Even though the magnetic moment of the antiproton is larger than that of the 3 He 30 nucleus, the former has a smaller overlap with the electron cloud. Therefore it creates 31 a smaller splitting. The complete hyperfine structure for p 3 He + is illustrated in Fig. 1.
3. Laser-microwave-laser spectroscopy 50 The first observation of a hyperfine structure in antiprotonic helium was achieved in  subsequently Auger decay of the transferred atoms and annihilation of the antipro-71 tons in the nucleus will occur. The number of annihilations after the second laser 72 pulse will be the larger the more antiprotons were transferred by the microwave pulse.

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When the antiprotons first enter the helium gas, a large annihilation peak ("prompt 75 peak") is caused by the majority of formed pHe + atoms which find themselves in Auger 76 decay-dominated states and annihilate within picoseconds after formation. At later 77 times, this peak exhibits an exponential tail due to pHe + atoms in the metastable  Since the intensity of the antiproton pulse fluctuates from shot to shot, the peaks 87 must be normalised by the total intensity of the pulse (total). This ratio is referred to 88 as peak-to-total. The peak-to-total (ptt) corresponds to the ratio of the peak area (I(t 1 ) 89 or I(t 2 )) to the total area under the full spectrum. If the second laser annihilation between antiprotonic helium atoms and regular helium atoms. Refilling from higher-98 lying states also contributes to the equalization of the hyperfine substate populations.

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In general, a short delay T is preferable because the signal height will decrease for 100 longer laser delay times as a result of the exponential decay of the metastable state 101 populations. However, the linewidth of the RF transition will increase if the delay is too 102 short. Further, far higher RF power will be required to complete one spin-flip. If the 103 delay is too long, the collisional relaxation of the system would already have eliminated 104 any asymmetry between the two states caused by the first laser pulse. The signal would 105 be too low to be observed.

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The two pulsed lasers were fixed to a wavelength of 723.877 nm, with a pulse  titanium window for the antiproton beam and a 4 mm thick fused silica window for the 135 laser beam to enter [23], and are equipped with meshes to contain the microwaves.

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In order to measure the annihilation decay products two Cherenkov counters are 137 mounted around the target volume, connected to photomultipliers (cf. Fig. 3) . They

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In preparation for the actual investigation of the hyperfine substructure, via microwave 158 resonance, several studies are required to optimize the parameters such as laser power, 159 laser resonance frequency, laser delay time and microwave power.   To fit the two transitions, a function of the natural line shape for a two-level system 210 which is affected by an oscillating magnetic field for a time T was used. It is given by [26] 211 Here X(ω) is the probability that an atom is transferred from one HF state to the other,  HF for the fitting of the raw data together with the reduced χ 2 /ndf and ν HF after inflating the errors of the individual data points by χ 2 /ndf . The fit transition frequencies are displayed for the two different fitting methods, ASF and ISF. At the higher resonance the frequency points differed slightly between 2010 and 2011. These data can only be combined in the averaging over all single scans. The microwave power for the 11.157 GHz resonance was further lower by about 2.5 W compared to 2011. Therefore, the values obtained by the ISF method were used as final results.   HF and ν −+ HF in comparison with three-body QED calculations, where ν HF denote the SSHF transition frequencies, δ exp is the relative error of the measured frequencies and Γ the resonance line width. The relative deviation of experiment and theory is defined as δ th−exp = (ν exp − ν th )/ν exp . The quoted theoretical precision is ∼ 5 × 10 −5 from the limitation of the Breit-Pauli approximation that neglects terms of relative order α 2 . This does not include numerical errors from the different variational methods used. For ref. [11]    such as microwave power, Q value and laser delay, the measured values were taken.

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To assess the rates of collisional effects which induce relaxations between the SSHF  Table 2), given as linear frequencies,  confirmed that the density dependence is very small. Also for p 3 He + theory predicts a 314 collisional shift at the kHz level, much smaller than the experimental error bars [17].

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For the frequency difference ∆ν ± HF = ν −+ HF −ν −− HF between the two SSHF lines around 316 11 GHz there is an agreement between both theoretical results and experiment within

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The two transitions at 16 GHz could not be measured anymore due to lack 325 of beamtime -even though the microwave target was readily tested and calibrated.

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However, we came to the conclusion that the observation of these two resonance lines 327 would deliver no additional information on the investigated three-body system and 328 primarily serve to accomplish a complete measurement of the p 3 He + hyperfine structure.

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This study with p 3 He + was considered a test of QED calculations using a more